The cooking of items by placing them on a grilling surface and simultaneously introducing steam into the interior of a hood covering food items being grilled is known as disclosed in U.S. Pat. No. 4,913,039. The grill disclosed in that patent is unevenly heated by either burning charcoal or lava rocks heated by an electric heating element or a gas flame, which is in contrast to the present invention where the grilling surface is evenly heated and whose temperature is accurately controlled, and, hence, the temperature of the cooking surface is accurately controlled.